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Fractional Brownian motion, random walks and binary market models

Tommi Sottinen ()

Finance and Stochastics, 2001, vol. 5, issue 3, 343-355

Abstract: We prove a Donsker type approximation theorem for the fractional Brownian motion in the case $H>1/2.$ Using this approximation we construct an elementary market model that converges weakly to the fractional analogue of the Black-Scholes model. We show that there exist arbitrage opportunities in this model. One such opportunity is constructed explicitly.

Keywords: Fractional Brownian motion; random walk; stock price model; binary market model (search for similar items in EconPapers)
JEL-codes: C60 G10 (search for similar items in EconPapers)
Date: 2001-07-12
Note: received: October 1999; final version received: August 2000
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